How Does Inserting a Dielectric Affect Capacitance and Potential?

[Arman777]

Homework Statement

Homework Equations

The Attempt at a Solution

I couldn't find the V(x).I don't know ho to write the equation.I think that it will be constant cause potential betwwen two plates should be constant... ?

 

[cnh1995]

What is the energy in the capacitor as a function of x?
In other words, what is the capacitance as a function of x?
How is force related to this energy?

 

[Arman777]

What is the energy in the capacitor as a function of x?
In other words, what is the capacitance as a function of x?
How is force related to this energy?

$C_{eq}=(K+1)ε_0 \frac {xb} {d}$ ? or maybe
$C=Kε_0 \frac {xb} {d}$

 

[cnh1995]

$C_{eq}=(K+1)ε_0 \frac {xb} {d}$ ? or maybe
$C=Kε_0 \frac {xb} {d}$

I don't know the exact expression as I myself haven't worked it out yet, but check the answer at x=0. Is the capacitance zero at x=0?

 

[Arman777]

I don't know the exact expression as I myself haven't worked it out yet, but check the answer at x=0. Is the capacitance zero at x=0?

Yeah its

 

[cnh1995]

Yeah its

No, it isn't.
What is the capacitance for x=0?

 

[Arman777]

No, it isn't.
What is the capacitance for x=0?

there's no area when x=0

 

[cnh1995]

there's no area when x=0

How is this possible? Which area is considered for calculation of capacitance?

 

[Arman777]

How is this possible? Which area is considered for calculation of capacitance?

You are taking a-x I am just x

 

[cnh1995]

You are taking a-x I am just x

But that doesn't make the total capacitance zero. You need to draw the equivalent circuit and find the total capacitance as a function of x.

 

[Arman777]

But that doesn't make the total capacitance zero. You need to draw the equivalent circuit and find the total capacitance as a function of x.

I didnt understand

 

[cnh1995]

I didnt understand

What is the dielectric between the plates before the new dielectric (with constant k) is inserted?
What is the capacitance when the new dielectric is not inserted at all?